A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points. Such fields model a number of physical properties, like velocity and temperature gradient in fluid flow, stress and momentum flux in elasticity.
Recently, line fields have earned eminence in the nematic fields ambiance [1]}, [2]}. In computer graphics, line field are common tools for quadrangulation [3]}, visualization of vector/line/symmetric tensor fields [4]}, [5]}, and remeshing [6]}. Curious line fields abound: some are illustrated in Figure REF . Fingerprints are studied by the pattern recognition community [7]}.
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